1,714 research outputs found
Geometric representation of interval exchange maps over algebraic number fields
We consider the restriction of interval exchange transformations to algebraic
number fields, which leads to maps on lattices. We characterize
renormalizability arithmetically, and study its relationships with a
geometrical quantity that we call the drift vector. We exhibit some examples of
renormalizable interval exchange maps with zero and non-zero drift vector, and
carry out some investigations of their properties. In particular, we look for
evidence of the finite decomposition property: each lattice is the union of
finitely many orbits.Comment: 34 pages, 8 postscript figure
Gauge Consistent Wilson Renormalization Group I: Abelian Case
A version of the Wilson Renormalization Group Equation consistent with gauge
symmetry is presented. A perturbative renormalizability proof is established. A
wilsonian derivation of the Callan-Symanzik equation is given.Comment: Latex2e, 39 pages, 3 eps figures. Revised version to appear in Int.
J. Mod. Phy
Hyperbolic outer billiards : a first example
We present the first example of a hyperbolic outer billiard. More precisely
we construct a one parameter family of examples which in some sense correspond
to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit
Thermodynamics of Kondo Model with Electronic Interactions
On the basis of Bethe ansatz solution of one dimensional Kondo model with
electronic interaction, the thermodynamics equilibrium of the system in finite
temperature is studied in terms of the strategy of Yang and Yang. The string
hypothesis in the spin rapidity is discussed extensively. The thermodynamics
quantities, such as specific heat and magnetic susceptibility, are obtained.Comment: 8 pages, 0 figures, Revte
Jorge A. Swieca's contributions to quantum field theory in the 60s and 70s and their relevance in present research
After revisiting some high points of particle physics and QFT of the two
decades from 1960 to 1980, I comment on the work by Jorge Andre Swieca. I
explain how it fits into the quantum field theory during these two decades and
draw attention to its relevance to the ongoing particle physics research. A
particular aim of this article is to direct thr readers mindfulness to the
relevance of what at the time of Swieca was called "the Schwinger Higgs
screening mechanism". which, together with recent ideas which generalize the
concept of gauge theories, has all the ingredients to revolutionize the issue
of gauge theories and the standard model.Comment: 49 pages, expansion and actualization of text, improvement of
formulations and addition of many references to be published in EPJH -
Historical Perspectives on Contemporary Physic
A simple analysis of halo density profiles using gravitational lensing time delays
Gravitational lensing time delays depend upon the Hubble constant and the
density distribution of the lensing galaxies. This allows one to either model
the lens and estimate the Hubble constant, or to use a prior on the Hubble
constant from other studies and investigate what the preferred density
distribution is. Some studies have required compact dark matter halos (constant
M/L ratio) in order to reconcile gravitational lenses with the HST/WMAP value
of the Hubble constant (72 +/- 8 km/s /Mpc and 72 +/- 5 km/s /Mpc,
respectively). This is in direct contradiction with X-ray, stellar dynamical,
and weak lensing studies, which all point towards extended halos and isothermal
density profiles. In this work, we examine an up-to-date sample of 13 lensing
galaxies resulting in a data set consisting of 21 time delays. We select
systems in which there is a single primary lensing galaxy (e.g. excluding
systems undergoing mergers). Analysis is performed using analytic models based
upon a powerlaw density profile (rho \propto r^-n) of which the isothermal
profile is a special case (n = 2). This yields a value of n = 2.11+/-0.12
(3sigma) for the mean profile when modeling with a prior on the Hubble
constant, which is only consistent with isothermality within 3 sigma. Note that
this is a formal error from our calculations, and does not include the impact
of sample selection or simplifications in the lens modeling. We conclude that
time delays are a useful probe of density profiles, in particular as a function
of the environment in which the lens resides, when combined with a prior on the
Hubble constant.Comment: A&A accepte
Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled Lattice Schwinger Model
We revisit the strong coupling limit of the Schwinger model on the lattice
using staggered fermions and the hamiltonian approach to lattice gauge
theories. Although staggered fermions have no continuous chiral symmetry, they
posses a discrete axial invari ance which forbids fermion mass and which must
be broken in order for the lattice Schwinger model to exhibit the features of
the spectrum of the continuum theory. We show that this discrete symmetry is
indeed broken spontaneously in the strong coupling li mit. Expanding around a
gauge invariant ground state and carefully considering the normal ordering of
the charge operator, we derive an improved strong coupling expansion and
compute the masses of the low lying bosonic excitations as well as the chiral
co ndensate of the model. We find very good agreement between our lattice
calculations and known continuum values for these quantities already in the
fourth order of strong coupling perturbation theory. We also find the exact
ground state of the antiferromag netic Ising spin chain with long range Coulomb
interaction, which determines the nature of the ground state in the strong
coupling limit.Comment: 24 pages, Latex, no figure
The Pivotal Role of Causality in Local Quantum Physics
In this article an attempt is made to present very recent conceptual and
computational developments in QFT as new manifestations of old and well
establihed physical principles. The vehicle for converting the
quantum-algebraic aspects of local quantum physics into more classical
geometric structures is the modular theory of Tomita. As the above named
laureate to whom I have dedicated has shown together with his collaborator for
the first time in sufficient generality, its use in physics goes through
Einstein causality. This line of research recently gained momentum when it was
realized that it is not only of structural and conceptual innovative power (see
section 4), but also promises to be a new computational road into
nonperturbative QFT (section 5) which, picturesquely speaking, enters the
subject on the extreme opposite (noncommutative) side.Comment: This is a updated version which has been submitted to Journal of
Physics A, tcilatex 62 pages. Adress: Institut fuer Theoretische Physik
FU-Berlin, Arnimallee 14, 14195 Berlin presently CBPF, Rua Dr. Xavier Sigaud
150, 22290-180 Rio de Janeiro, Brazi
Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
The superselection sectors of two classes of scalar bilocal quantum fields in
D>=4 dimensions are explicitly determined by working out the constraints
imposed by unitarity. The resulting classification in terms of the dual of the
respective gauge groups U(N) and O(N) confirms the expectations based on
general results obtained in the framework of local nets in algebraic quantum
field theory, but the approach using standard Lie algebra methods rather than
abstract duality theory is complementary. The result indicates that one does
not lose interesting models if one postulates the absence of scalar fields of
dimension D-2 in models with global conformal invariance. Another remarkable
outcome is the observation that, with an appropriate choice of the Hamiltonian,
a Lie algebra embedded into the associative algebra of observables completely
fixes the representation theory.Comment: 27 pages, v3: result improved by eliminating redundant assumptio
Renormalization Group Study of Chern-Simons Field Coupled to Scalar Matter in a Modified BPHZ Subtraction Scheme
We apply a soft version of the BPHZ subtraction scheme to the computation of
two-loop corrections from an Abelian Chern-Simons field coupled to (massive)
scalar matter with a and
self-interactions. The two-loop renormalization group functions are calculated.
We compare our results with those in the literature.Comment: 15 pages, 7 figures, revtex. To appear in Phys. Rev.
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